论文标题
在$ c^*$ - 代数的起重属性上
On the Lifting Property for $C^*$-algebras
论文作者
论文摘要
我们表征了可分离的$ c^*$ - 代数$ a $的提升属性（LP），其最大张量产品与其他$ c^*$ - 代数 - 不，我们证明$ a $ a $在任何家庭$（\ can in i Mid can $ can $ c^$ can $ c^$ can $ can）时才证明$ a $ a $ a $ a $ a $ a $ a $ - {\ ell_ \ infty（\ {d_i \}）\ otimes _ {\ max} a} \ to {\ ell_ \ infty（\ {d_i \ otimes _ {\ otimes _ {\ \ axmax} a = m \ otimes _ {\ rm nor} a $对于任何von Neumann代数$ m $。
We characterize the lifting property (LP) of a separable $C^*$-algebra $A$ by a property of its maximal tensor product with other $C^*$-algebras, namely we prove that $A$ has the LP if and only if for any family $(\{D_i\mid i\in I\}$ of $C^*$-algebras the canonical map $$ {\ell_\infty(\{D_i\}) \otimes_{\max} A}\to {\ell_\infty(\{D_i \otimes_{\max} A\}) }$$ is isometric. Equivalently, this holds if and only if $M \otimes_{\max} A= M \otimes_{\rm nor} A$ for any von Neumann algebra $M$.
